jake watched a stock car race with his dad. after the race, the television showed the average speed of each…

Answer:

To determine the correct box - plot, we need to find the five - number summary (minimum, first quartile $Q_1$, median, third quartile $Q_3$, maximum) of the data set ${100,114,117,121,110,120,130,103,111,116}$.

Step1: Sort the data

First, sort the data in ascending order: ${100,103,110,111,114,116,117,120,121,130}$.

Step2: Find the minimum and maximum

The minimum value is $100$ and the maximum value is $130$.

Step3: Find the median

Since there are $n = 10$ data points, the median is the average of the $\frac{n}{2}=5$th and $\frac{n}{2}+ 1=6$th ordered values. Median $=\frac{114 + 116}{2}=115$.

Step4: Find $Q_1$

The lower half of the data is ${100,103,110,111,114}$. Since $n_1 = 5$ (odd number of data points in the lower half), $Q_1$ is the $\frac{n_1 + 1}{2}=3$rd value in the lower - half. So $Q_1 = 110$.

Step5: Find $Q_3$

The upper half of the data is ${116,117,120,121,130}$. Since $n_2=5$ (odd number of data points in the upper half), $Q_3$ is the $\frac{n_2 + 1}{2}=3$rd value in the upper - half. So $Q_3 = 120$.

The box - plot should have a whisker starting at $100$, the left - hand side of the box at $110$, the line inside the box at $115$, the right - hand side of the box at $120$, and the other whisker ending at $130$. Without seeing the full options, you can check which box - plot has these values marked correctly.

(Note: Since the box - plots in the image are not fully described with values on them, the above is the general process to find the correct box - plot for the given data set).